Question

A) which triangle is congruent to PQRB)Name the set of rigid motions that moves PQR to the congruent triangle

Answer 1

a) By inspection, we can see that triangles JKL and STU are larger than triangle PQR. The triangle that is congruent with triangle PQR is triangle DEF.

b) The congruence can be proven by providing the set of rigid motions that moves PQR to triangle DEF. If we do a clockwise rotation of 90 degrees around the origin, the coordinate number changes into:

`(x,y)\rightarrow(x,-y)`

The triangle PQR has the coordinates P (2, 4), Q(5, 6), and R(4, 3). The change in coordinates using the clockwise rotation of 90 degrees around the origin will be:

`\begin{gathered} P(2,4)\rightarrow(2,-4) \\ Q(5,6)\rightarrow(5,-6) \\ R(4,3)\rightarrow(4,-3) \end{gathered}`

The coordinates of the triangle DEF are D(2, -4), F(4,-3), and E(5,-6), which are the same as the transformation of the triangle PQR via 90 degrees clockwise rotation about the origin.

Answers:

a) Triangle DEF

b) clockwise rotation of 90 degrees around the origin